Welcome to Code Jam (Hard)

Note that this is a harder version of the problem
welcomeeasy.

So you’ve registered. We sent you a welcoming email, to
welcome you to code jam. But it’s possible that you still don’t
feel welcomed to code jam. That’s why we decided to name a
problem “welcome to code jam.” After solving this problem, we
hope that you’ll feel very welcome. Very welcome, that is, to
code jam.

If you read the previous paragraph, you’re probably
wondering why it’s there. But if you read it very carefully,
you might notice that we have written the words “welcome to
code jam” several times: $400\,
263\, 727$ times in total. After all, it’s easy to look
through the paragraph and find a ‘w’; then find an ‘e’ later in
the paragraph; then find an ‘l’ after that, and so on. Your
task is to write a program that can take any text and print out
how many times that text contains the phrase “welcome to code
jam”.

To be more precise, given a text string, you are to
determine how many times the string “welcome to code jam”
appears as a sub-sequence of that string. In other words, find
a sequence $s$ of
increasing indices into the input string such that the
concatenation of $\textrm{input}[s[0]], \textrm{input}[s[1]],
\dots , \textrm{input}[s[18]]$ is the string “welcome to
code jam”.

The result of your calculation might be huge, so for
convenience we would only like you to find the last
$4$ digits.

Input

The first line of input gives the number of test cases
$T, 1 \le T \le 100$. The
next $N$ lines of input
contain one test case each. Each test case is a single line of
text of length at most $500$, containing only lower-case
letters and spaces. No line will start with a space, and no
line will end with a space.

Output

For each test case, “Case #$x$: $dddd$”, where $x$ is the case number, and
$dddd$ is the last four
digits of the answer. If the answer has fewer than $4$ digits, please add zeroes at the
front of your answer to make it exactly 4 digits long.